Chapter 4

Polynomial and Rational Functions

Materials on this page are sorted based on objectives you will need to master, rather than a lesson in the book. Click on the objective to jump to the related links and handouts.

To be successful with this chapter you will need to master the following skills:

Skill	Review in the book	Additional Resources	video tutorials
Factor polynomial expressions		worksheet on special products Factoring Quadratic Trinomials Factoring Quadrating trinomials harder	Factoring Special Products Factoring Trinomials with a>1 Factoring Trinomials by trial and error more factoring Factor Perfect Squares Factor Difference of Squares
Degree, leading coefficient, and polynomials	A23-30		intro to polynomials
Simplify polynomials using distributive property and FOIL		Multiplying polynomials	adding, subtracting, and multiplying polynomials multiplying polynomials
Divide polynomials using long or synthetic division	A26-A28 all examples A31-A34, #5-26		Long Division Long division harder Ex Synthetic Division Synthetic Division Ex. 2 Factoring polynomial using synthetic division
Graphing Functions (T-chart, plotting points, finding intercepts)
Simplifying algebraic fractions		Worksheet	Adding rational Expressions ex 2 Adding and subtracting rational exp. Ex 1 Adding and subtracting rational expressions Multiplying and dividing Ex 1 Multiplying and dividing Ex 2 Multiplying and Dividing Ex 3
Finding domain of the function		Find excluded values
solving linear and quadratic equations	A50, Examples 4,5 A53, Examples 8,9 A57, Example 12 A58, #65-74, 87-92
operations with complex numbers (addition, multiplication, conjugate)		worksheet	Simplifying radicals into complex numbers Adding and Subtracting Complex Numbers Simplifying powers of i Multiplying Complex Numbers Multiplying complex numbers 2 What are complex numbers?
solving quadratic equations over complex numbers			Solving quadratic equation over complex numbers

Objective	Related lesson in the book	Exercises in the book	Additional Resources
Identify polynomial functions	4.1		http://youtu.be/Lc9O-1joI24
Identify the degree of the polynomial	4.1
Identify end behavior of the function based on odd or even power function	4.1
Identify roots of the function and their multiplicity	4.1		finding zeros of the polynomials Finding the zeros and factoring polynomials
Find polynomial function based on the given roots and their multiplicity	4.1		graphing functions 4.1 review.pdf Details Download 407 KB graphing functions 4.1 review p.2.pdf Details Download 610 KB graphing polynomial function ex 1
Identify domain of a rational functions	4.2		Domain of a Rational Function
Identify horizontal, vertical, and oblique asymptotes of a rational function	4.2		Find VA, HA, and OA Find intercepts and asymptotes
Sketch a graph of rational function using VA, HA, OA	4.3		http://home.windstream.net/okrebs/page192.html Graphing Rational Functions Ex 1 Graphing Rational Functions Ex 2 Graphing Rational Functions Ex. 3 Graphing Rational functions Ex. 4 Graphing Rational Functions Ex. 5 (with OA) Graphing Rational Functions Ex. 6 More tutorials on graphing rational functions (more videos listed on the right) Graphing Rational Functions -check yourself
Sketch graph of a polynomial function using roots+multiplicity and degree	4.4		http://www.youtube.com/watch?v=j8H7gYo-HKs http://www.onlinemathlearning.com/graphing-polynomials.html
Solve polynomial inequality using sketch of the graph	4.4
Solving Inequalities using interval method (algebraically)	4.4		rational inequalities Rational inequalities Ex. 2
Identify maximum number of real roots	4.5
Identify potential rational zeros	4.5		http://youtu.be/QHTC-RJH-b4 http://www.youtube.com/watch?v=9dBUnjwMgtY
Factor polynomials using Conjugate Pairs and Rational Roots theorems	4.6		Factoring Polynomial using a given complex root How to use Conjugate Pairs Theorem Factoring Polynomial completely Factoring Polynomial completely Ex 2 Finding all the zeros of the polynomial
Solve polynomial equations over complex numbers by factoring Intermediate Value Theorem	4.6		How to apply IVT
15. Solve rational inequalities using graph of function or algebraically	4.4		rational inequalities1.pdf Details Download 533 KB rational inequalities 2.pdf Details Download 443 KB
Review of the Chapter		test review Ch 4.pdf Details Download 625 KB	answer key ch 4 review key page1.pdf Details Download 4 MB ch4review.pdf Details Download 397 KB Another great review summary and practice test (multiple choice): Polynomial and Rational Functions Review

Study guide for the chapter test:
1. Read the objectives and ask yourself you can perform all the tasks outlined above.
2. The following problems from your text book resemble the questions on the test:
page 241-242: #1-4; #11-18 (graph using zeros, multiplicity, end behavior); #19-22; #23-34 (graph using intercepts, asymptotes, and additional points); #35-44 (write solution in interval form and show it on the number line); #45-48; #51-52; #53-58; #75-78; #79-86 (use rational zeros theorem to guess and check possible roots)
You can submit your review work for extra credit! However, it will only count if you showed every step of the solution.